Question

In an A.P., ten times of its tenth term is equal to thirty times of its 30${}^{th}$ term. Find its 40${}^{th}$ term.

Answer 1

'a' be the first term and having 'd' as common difference.

$\therefore T_{{10}^{th}}=a+9d$

$T_{30}=a+29d$

$\therefore 10\times (a+9d)=30\times (a+29d)$

$10a+90d=30a+870d$

$20a+780d=0$ ………..$\left(1\right)$

$T_{40}=a+39d$

$20\times T_{40}=20a+780d$

$=0$

$\therefore T_{40}=0$.